psn_linalg.c

Finite Volume Poisson PDE Solver

/*psn_lib/psn_linalg.c*/
/***********************************************************************
    Finite Volume Poisson PDE Solver: C-Library & Matlab Toolbox
    Implements numerical solution of Poisson PDE
    in 2D  Cartesian and Cylindrical coordinates

    Copyright (C) 2004 Igor Kaufman
    Copyright (C) 2004 Lancaster University, UK

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA


    Author's email: [e-mail]

    APPLICATION    : COMMON ROUTINES
    VERSION        : 1.0
************************************************************************/
/*17.01.04*/

#include "psn.h"

/*
Function to invert tridiagonal matrix equation.
Left, centre, and right diagonal elements of matrix
stored in arrays a, b, c, respectively.
Right-hand side stored in array w.
Solution written to array u.

Matrix is NxN. Arrays a, b, c, w, u assumed to be of extent N+2,
with redundant 0 and N+1 elements.
Code source:http://farside.ph.utexas.edu/teaching/329/lectures/node77.html
*/


int psn_tridiag_solve_low(
   const size_t N,
   const PSN_VECTOR a,
   PSN_VECTOR b,
   const PSN_VECTOR c,
   PSN_VECTOR u
)
{
      size_t i,k;

      if (b[1]==0) return 2;

      for (i = 2,k=1; i <=N; i++,k++)  {
        double t = a[i]/b[k];
        b[i]-= t*c[k];
        u[i]-= t*u[k];
        if (b[i]==0) return 2;
      }

      u[N]/= b[N];
      for (i = N - 1;i>0; i--) {
        u[i]-=c[i]*u[i+1];
        u[i]/=b[i];
      }
      return 0;
}

int psn_tridiag_solve_std(
   const size_t N,
   const PSN_VECTOR a,
   const PSN_VECTOR b,
   const PSN_VECTOR c,
   const PSN_VECTOR w,
   PSN_VECTOR u
)
{
   size_t i;
   int res;

   PSN_VECTOR b1=psn_vector_create(N+2);
   if (!b1) return 1;
   for (i=0;i<N+1;i++) {
     b1[i]=b[i];
     u[i]=w[i];
   }
   res=psn_tridiag_solve_low(N,a,b1,c,u);
   psn_vector_free(b1);

   return res;

}